Chapter 12.1, Problem 68AYU

In Problems 61-70, express each sum using summation notation.

$a+ar+a{r}^2+\mathrm{...}+a{r}^{n-1}$

To determine

To find: The sum using summation notation: $a+ar+a{r}^2+\dots \dots \mathrm{..}+a{r}^{n-1}$.

Answer to Problem 68AYU

$a+ar+a{r}^2+\dots \dots \mathrm{..}+a{r}^{n-1}={\displaystyle \sum }_{k=1}^{n}a{r}^{k-1}$

Explanation of Solution

Given:

$a+ar+a{r}^2+\dots \dots \mathrm{..}+a{r}^{n-1}$

Calculation:

$a+ar+a{r}^2+\dots \dots \mathrm{..}+a{r}^{n-1}={\displaystyle \sum }_{k=1}^{n}a{r}^{k-1}$